User talk:Paul Wormer/scratchbook

A physical system is the part of the universe that a physicist is interested in. Physics is a reductionist science meaning that a physicist restricts his studies to that part of the universe that is as simple as possible and yet shows—as far as he can see—all the physical phenomena that are essential to his study. This delimitation of his object of study is a conditio sine qua non in understanding and explaining his observations.

Hand in hand with reduction go idealization and abstraction. Non-physicists are amused by the idealizations commonly applied in physics. Many have heard in high school of the proverbial infinitely thin, infinitely strong, yet massless, rope from which hangs a heavy mass of infinitely small diameter. Many non-physicists are deterred by the abstractions that have entered physics over the last three centuries. What does it mean that a physical system strives for maximum entropy or that a wave function of a system collapses when measurements are performed on it? What exactly vibrates when a radio signal is emitted? It takes physics students quite some time and effort before they can visualize in their minds these concepts. Interested laymen are often irritated by the abstractions of physicists that they conceive as unnecessary Wichtigmacherei (making important).

When a physicist separates part of the universe as his physical system, i.e., as his object of study, then he must define at the same time the variables that determine the state of the system. Without the concept of state the concept of physical system is valueless. When Newton considered around 1666 his physical system to consist of the point masses Sun and Earth, he simultaneously assumed that the state of this system is uniquely determined by the position and the velocity of the Earth. In this he made the idealizing assumptions that the Sun is at rest and that the diameters of Sun and Earth are of no importance and may be set equal to zero. (When Newton later explained the origin of the tides, the diameter of the Earth became, of course, non-negligible).

Most physical states are non-stationary, they develop in time. The pertinent parameters, which—by another idealization—are assumed to be observable (measurable), change in time. The main purpose of physics is to discover the laws that describe the development in time of the state of the physical system. When a physicist sets himself to the task of discovering these laws, he makes the assumption that the time development of a state is causal, that is to say, that a state at certain time uniquely fixes the state of the same system at a later time. Further he will search for the mathematical equation that will describe the time development. This is the equation of motion of the physical system. Newton discovered by his study of two attracting masses his famous second law F = m a and Schrödinger discovered HΨ= i dΨ/dt for the causal development of the wave function Ψ of a system consisting of microscopic quantum particles.

We saw that a physical system does not have to be separated mechanically from the universe. Indeed, it is evident that Newton did not put the Sun and the Earth inside a vessel with adiabatic walls, in other words, a physical system is not necessarily physically isolated from his environment. However, in practice it can be very convenient if it is separated, because it will aid the interpretation and explanation of measurements when one is assured that certain interactions with the surroundings are not present.

It is usually not easy for an experimentator to separate a physical system from the rest of the universe. For instance, a physical chemist studying a system consisting of molecules will try to observe only the molecules that he is interested in, and will try to reduce the number of other molecules. Thus, he needs very thorough purification and/or high vacuum. He will also try to shield the molecules from unwanted external fields, such as electrostatic, magnetic, and gravitational fields. (The latter field cannot be shielded, but weightless conditions are possible in space stations). For a theoretician, on the other hand, the definition of an isolated physical system is trivial, it is just the part of the universe (matter and fields) that he considers in his equations.

The conceptually most important physical system is the closed system, where it assumed that there is no interaction with the rest of the universe. No energy or matter can flow in or out of a closed system. Obviously, completely closed systems are of no interest to experimental physicists, because no signals will leave such a system and he will not be able to manipulate the system because no signals will enter a closed system either. Thus, in the laboratory, physical systems are always partly open. For a theoretician the idealizing concept of closed system is of great importance and almost always applied, even in studies of open systems. For instance, when a thermodynamicist considers a system that is in temperature equilibrium with its environment (an open system, heat may flow in and out), he will assume it to be in a very large heat bath and the original system plus the heat bath is then again a closed physical system.